The motivation for this paper is to account for subject specific variations in a Cox proportional hazard model for alternating recurrent events. This is done through two sets of frailty components, whose marginal distributions are bound together by a copula function. The likelihood function involves unobservable variables, which requires the use of the EM algorithm. This leads to intractable integrals, which after some approximations, are solved using computationally intensive techniques. The results are applied to a real-life data. A simulation study is also carried out to check for consistency.